Uncertainty and error in computational simulations

The present paper addresses the question: ``What are the general classes of uncertainty and error sources in complex, computational simulations?`` This is the first step of a two step process to develop a general methodology for quantitatively estimating the global modeling and simulation uncertainty in computational modeling and simulation. The second step is to develop a general mathematical procedure for representing, combining and propagating all of the individual sources through the simulation. The authors develop a comprehensive view of the general phases of modeling and simulation. The phases proposed are: conceptual modeling of the physical system, mathematical modeling of the system, discretization of the mathematical model, computer programming of the discrete model, numerical solution of the model, and interpretation of the results. This new view is built upon combining phases recognized in the disciplines of operations research and numerical solution methods for partial differential equations. The characteristics and activities of each of these phases is discussed in general, but examples are given for the fields of computational fluid dynamics and heat transfer. They argue that a clear distinction should be made between uncertainty and error that can arise in each of these phases. The present definitions for uncertainty and error are inadequate and. therefore, they propose comprehensive definitions for these terms. Specific classes of uncertainty and error sources are then defined that can occur in each phase of modeling and simulation. The numerical sources of error considered apply regardless of whether the discretization procedure is based on finite elements, finite volumes, or finite differences. To better explain the broad types of sources of uncertainty and error, and the utility of their categorization, they discuss a coupled-physics example simulation